Simple Bond-Charge Model for Symmetric Stretching Vibrations of XYn Molecules

Abstract

A bond‐charge model, previously applied to homonuclear and heteronuclear diatomic species has been extended to symmetric XY_n polyatomic molecules. The chief theoretical tool is the scaled form of the molecular virial theorem. Using this theorem, we relate the force constant for symmetric breathing vibrations to model expressions for the electronic kinetic and potential energies. As in the diatomic case, the kinetic energy is modeled as a particle in a box and the potential energy as a classical system of point charges. Using experimental force constants and bond lengths as input we have evaluated the model bond‐charge and path‐length parameters for 30 polyatomic species. The bond‐charge parameter $q$ is reasonably interpreted as a measure of bond order while the free‐electron path‐length parameter $\nu$ is a measure of atomic core radii. Values of $q$ and $\nu$ are given for ground‐state and electronically excited‐state molecules as well as charged molecular ions, in symmetries $D_{\mathrm{\infty h}}{\mathrm{,\; D}}_{\text{3h}}{\mathrm{,\; C}}_{\text{2υ}}{\mathrm{,\; C}}_{\text{3υ}}$ , and $T_d$ . The path‐length parameter $\nu$ is shown to correlate with position of the constituent atoms in the periodic chart. It is then shown that polyatomic $\nu$ values can be predicted accurately from $\nu$ values of homonuclear diatomic molecules. This latter result permits the possibility of predicting force constants from input of bond lengths only, and some results of this type are presented.